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Embedding geometry plays a fundamental role in retrieval quality, yet dense retrievers for retrieval-augmented generation (RAG) remain largely confined to Euclidean space. However, natural language exhibits hierarchical structure from broad…

Backward compatible representation learning enables updated models to integrate seamlessly with existing ones, avoiding to reprocess stored data. Despite recent advances, existing compatibility approaches in Euclidean space neglect the…

We prove that there is a randomized polynomial-time algorithm that given an edge-weighted graph $G$ excluding a fixed-minor $Q$ on $n$ vertices and an accuracy parameter $\varepsilon>0$, constructs an edge-weighted graph~$H$ and an…

In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…

We present the first non-trivial fully dynamic algorithm maintaining exact single-source distances in unweighted graphs. This resolves an open problem stated by Sankowski [COCOON 2005] and van den Brand and Nanongkai [FOCS 2019]. Previous…

We propose a space-time scheme that combines an unfitted finite element method in space with a discontinuous Galerkin time discretisation for the accurate numerical approximation of parabolic problems with moving domains or interfaces. We…

Adiabatic quantum algorithms must evolve slowly enough to suppress non-adiabatic transitions while remaining fast enough to be practical. In open systems, this trade-off is reshaped by decoherence. For Hamiltonians subject to dephasing…

The $K$-core of a graph is the unique maximum subgraph within which each vertex connects to $K$ or more other vertices. The optimal $K$-core attack problem asks to delete the minimum number of vertices from the $K$-core to induce its…

We present a new and surprisingly simple analysis of random-shift decompositions -- originally proposed by Miller, Peng, and Xu [SPAA'13]: We show that decompositions for exponentially growing scales $D = 2^0, 2^1, \ldots,…

We connect the mixing behaviour of random walks over a graph to the power of the local-consistency algorithm for the solution of the corresponding constraint satisfaction problem (CSP). We extend this connection to arbitrary CSPs and their…

Ergodicity breaking in isolated systems has emerged as an important frontier in the study of quantum many-body physics. While generic Hamiltonians are expected to obey the eigenstate thermalization hypothesis (ETH), recent studies on…

Efficiently computing accurate representations of high-dimensional data is essential for data analysis and unsupervised learning. Dendrograms, also known as ultrametrics, are widely used representations that preserve hierarchical…

We propose a new paradigm for designing efficient p-adaptive arbitrary high order methods. We consider arbitrary high order iterative schemes that gain one order of accuracy at each iteration and we modify them in order to match the…

We give an algorithm that, given an $n$-vertex graph $G$ and an integer $k$, in time $2^{O(k)} n$ either outputs a tree decomposition of $G$ of width at most $2k + 1$ or determines that the treewidth of $G$ is larger than $k$. This is the…

We present and analyze a new space-time parallel multigrid method for parabolic equations. The method is based on arbitrarily high order discontinuous Galerkin discretizations in time, and a finite element discretization in space. The key…

The Cut & Count technique and the rank-based approach have lead to single-exponential FPT algorithms parameterized by treewidth, that is, running in time $2^{O(tw)}n^{O(1)}$, for Feedback Vertex Set and connected versions of the classical…

In this paper, we consider the Cycle Packing problem on unit disk graphs defined as follows. Given a unit disk graph G with n vertices and an integer k, the goal is to find a set of $k$ vertex-disjoint cycles of G if it exists. Our…

Time-periodic weak solutions for a coupled hyperbolic-parabolic system are obtained. A linear heat and wave equation are considered on two respective $d$-dimensional spatial domains that share a common $(d-1)$-dimensional interface…

Bayesian inference problems require sampling or approximating high-dimensional probability distributions. The focus of this paper is on the recently introduced Stein variational gradient descent methodology, a class of algorithms that rely…

Forecasting chaotic dynamics beyond a few Lyapunov times is difficult because infinitesimal errors grow exponentially. Existing Echo State Networks (ESNs) mitigate this growth but employ reservoirs whose Euclidean geometry is mismatched to…